1967 IMO Problems/Problem 2
Prove that iff. one edge of a tetrahedron is less than ; then its volume is less than or equal to .
Assume and let . Let be the feet of perpendicular from to and and from to , respectively.
Suppose . We have that , . We also have . So the volume of the tetrahedron is .
We want to prove that this value is at most , which is equivalent to . This is true because .
The above solution was posted and copyrighted by jgnr. The original thread can be found here: 
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